d_eff in PINNs is shown to be an operator invariant equal to kernel dimension for finite-kernel operators, enabling subspace projection for physics-preserving constraint adaptation.
On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs
6 Pith papers cite this work. Polarity classification is still indexing.
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Proves first UATs for k-times differentiable nonlinear operators and their derivatives via OL architectures uniformly on compact sets in weighted Bastiani-Sobolev spaces on general Banach spaces.
Establishes convergence for non-Lipschitz generators via bounded double-well lemma and truncated BSDE analysis, plus XNet architecture for efficient 100D PDE computation.
Tr-PINNs corrects boundary errors in PINNs for non-homogeneous 2D Navier-Stokes equations and supplies error analysis derived from the non-homogeneous Stokes problem.
PINNSur applies PINNs to surface PDEs by neural approximation of normals and operator projection, with an added empirical test for convergence behavior.
A systematic review of Kolmogorov-Arnold Networks that maps their relation to Kolmogorov superposition theory, MLPs, and kernels, examines basis-function design choices, summarizes performance advances, and supplies a practitioner's selection guide plus open challenges.
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Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks
d_eff in PINNs is shown to be an operator invariant equal to kernel dimension for finite-kernel operators, enabling subspace projection for physics-preserving constraint adaptation.
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Universal Approximation of Nonlinear Operators and Their Derivatives
Proves first UATs for k-times differentiable nonlinear operators and their derivatives via OL architectures uniformly on compact sets in weighted Bastiani-Sobolev spaces on general Banach spaces.
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Error Analysis of Tr-PINNs Algorithm for 2D Incompressible Navier-Stokes Equations with Non-Homogeneous Boundary Conditions
Tr-PINNs corrects boundary errors in PINNs for non-homogeneous 2D Navier-Stokes equations and supplies error analysis derived from the non-homogeneous Stokes problem.
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PINNsur: Physics-Informed Neural Networks for PDEs on Curved Surfaces
PINNSur applies PINNs to surface PDEs by neural approximation of normals and operator projection, with an added empirical test for convergence behavior.